Fast implementation of a l_∞- l/₁ penalized sparse representations algorithm: applications in image denoising and coding

Sparse representation techniques have become an important tool in image processing in recent years, for coding, de-noising and in-painting purposes, for instance. They generally rely on an lscr₂-lscr₁ penalized criterion and fast algorithms have been proposed to speed up the applications. We propose to replace the lscr₂-part of the criterion, which has been chosen both for its easy implementation and its relation to the PSNR quality measure, by a lscr_∞-part. We present a new fast way to minimize a lscr_∞- lscr₁ penalized criterion and assess its potential benefits for image De-noising and coding.